I finally started reading your paper. The math is beyond me for now. I'm reading it like a novel.
I am very sorry to hear that. I was under the impression you had a Ph.D. in physics. If that were the case, none of the math should be outside your experience; however, I have noticed, in recent years, that things which were obvious to me 20 years ago are far from obvious today (to be explicit, some of that stuff in chapter 5 needs a little more defense than what I put forward)so maybe I should be sympathetic.
You say that you can add any constant to the data. But if I think of some typical examples of data, like temperature or mass or charge, you cannot add a constant to them without changing the universe as scientists seem to think.
What you omit is the fact that the “knowable data” must completely exhaust all that is knowable. This means that the data you need to work with must include all the information necessary to give definition to those concepts “temperature”, “mass”, “charge” and all the associated concepts. If you think of all this information as being imbedded in that “set of numbers” which I define as the representation of the “knowable data” in the form of a secret code, adding a constant seems to be quite a trivial distortion to unravel.
Secondly, if you follow the development of my model of that knowable data carefully, you will comprehend that the concepts “temperature”, “mass”, “charge” together with many other similar concepts actually arise through the “unknowable” contribution: the fictional data created by my imagination to explain that “knowable” data. At this point, it is very important that you carefully follow the entire thread
as it contains discussion of some of the subtle issues arising from the fact that the set of concepts in one man’s representation may not map into exactly the same concepts in another representation. What is really significant is that the two representations are isomorphic.
Does this possibly constrain your theory to data that can have both plus and minus values?
Yes it does! However, do not fail to observe that, if the only information available to you is the set of numbers you have received (that is, there exists no absolutely no information about this data which can be obtained by any means other than being embedded in that data expressed by the numbers) just exactly how do you intend to prove that a negative number will never arise in a new example of that data stream. So, is this a constraint or is it acceptance of all possibilities. (Certainly if you accept that addition of a constant does not destroy the information content of the code, the whole question becomes moot.)
Early in your analysis you use a series of constraints and approximations, but at the end of the chapter you say your theory has no constraints. Have I missed something?
Since I do not know exactly which statements you are referring to, you will have to bring them up issue by issue and I will do my best to explain exactly what I mean. By the way, that's my "model", not my theory. The model has no constraints from the perspective that there exists no data which cannot be cast into the model: i.e., all possibilities are representable.
The use of the exponential to express many quantities seems fundamental to your results. When I stop reading and get down to thinking that is the first aspect I want to understand the significance of.
The exponential is a very important function in physics due to the fact that it is the solution to the differential equation expressed by the idea that the differential of a function is the function itself. More of those feedback relations (do the idea circular reasoning strike a bell)! You should be aware that the exponential function is isomorphic to the trig functions so that any time waves occur we are talking about a differential equation which admits of an exponential solution. Anytime probability is independent of position, the only possible relationship between position and probability must be via an exponential function (no other function will fulfill the constraints implied by the question).
Much of this is straight out of mathematical proofs hundreds of years old. I hope I have cleared it up a little.
Have fun -- Dick